[9] R Ã : (1) x 0 R A(x 0 ) = 1; (2) α [0 1] Ã α = {x A(x) α} = [A α A α ]. A(x) Ã. R R. Ã 1 m x m α x m α > 0; α A(x) = 1 x m m x m +

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Download "[9] R Ã : (1) x 0 R A(x 0 ) = 1; (2) α [0 1] Ã α = {x A(x) α} = [A α A α ]. A(x) Ã. R R. Ã 1 m x m α x m α > 0; α A(x) = 1 x m m x m +"

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1 Chinese Journal of Applied Probability and Statistics Vol.28 No.6 Dec ( ) Euclidean Lebesgue... :. : O212.2 O Zadeh [1 2]. Tanaa (1982) ; Diamond (1988) (FLS) FLS LS ; Savic Pedrycz (1991) FLS ; Chang (2001).. [7]. Euclidean Lebesgue. ( ) (BK )

2 [9] R Ã : (1) x 0 R A(x 0 ) = 1; (2) α [0 1] Ã α = {x A(x) α} = [A α A α ]. A(x) Ã. R R. Ã 1 m x m α x m α > 0; α A(x) = 1 x m m x m + β β > 0; β 0 Ã (m α β). α = β Ã (m α). : 2.1 [10] (1) Ã = ( a m a l a r ); Ã = (a m a l a r ) B = (b m b l b r ) (2) Ã + B = (a m + b m a l + b l a r + b r ); (3) Ã B = (a m b m a l + b l a r + b r ); (4) tã = (ta m t a l t a r ) t R. ( ỹ i ) (i = n) ỹ i R. ỹ = β 0 + β 1 x β0 β 1 R. (2.1) β 0 β 1 d ( ỹ i ) (i = n) min φ( β 0 β 1 ) = n d 2 (ỹ i β 0 + β 1 ). φ( β δ β0 0 β 1 ) = 0 φ( β δ β1 0 β 1 ) = 0 R.

3 : Euclidean Lebesgue. 2.2 [10] (Euclidean ) Ã B Ã = (a m a l a r ) B = (b m b l b r ) d 2 E(Ã B) = (a m b m ) 2 ω m + (a l b l ) 2 ω l + (a r b r ) 2 ω r (2.2) ω m > 0 ω l > 0 ω r > 0. Ã = (a α) B = (b β) d 2 E(Ã B) = (a b) 2 + (α β) 2. (2.3) (2.2) d 2 E (Ã B) ( R d 2 E ). 2.3 [11] (Lebesgue ) Ã B (Ã = (a (λ) a + (λ)) B = (b (λ) b + (λ)) d(ã B) ( 1 1/2 = f(λ)d 2 (A λ B λ )dλ) (2.4) 0 Ã = A λ = (a (λ) a + (λ)) B = Bλ = (b (λ) b + (λ)) Ã B λ Ã = A λ = {u µã(u) λ 0 λ 1} B = Bλ = {u µ B(u) λ 0 λ 1} µã(u) µ B(u) Ã B. d 2 (A λ B λ ) = (a (λ) b (λ)) 2 + (a + (λ) b + (λ)) 2 f(λ) [0 1] f(0) = f(λ)dλ = 1/2. (2.4) f(λ) = λ : 2.4 Ã = (a m a l a r ) B = (b m b l b r ) d(ã B) = ([a m b m + (a l b l )] 2 + [a m b m (a l b l )] 2 + (a m b m ) 2 ) 1/2 Ã B. Ã B d(ã B) = (3(a m b m ) 2 + 2(a l b l ) 2 ) 1/2 a l = a r b l = b r.

4 ỹ = β 0 + β 1 x β 0 R β 1 R 2.1 ỹ = β 0 + β 1 x ( ỹ i ) i = n ỹ i = (y i l i r i ) i = n β 0 = n n y i n n y i n n ( n ) 2 : β 1 = (β 1 β 1l β 1r ) n n y i n n y i β 1 = n n ( n ) 2 n l i n n r i n. φ(β 0 β 1 ) = n d 2 E(ỹ i β 0 + β 1 ) = n [(y i β 0 β 1 ) 2 + (l i β 1l ) 2 + (r i β 1r ) 2 ] φ = 2 β 0 n (y i β 0 β 1 ) = 0 φ = 2 n (y i β 0 β 1 ) = 0 β 1 φ = 2 n (l i β 1l ) = 0 β 1l φ = 2 n (r i β 1r ) = 0. β 1r n n x 2 i y i n n y i β 0 = n n ( n ) 2 n n y i n n n y i l i β 1 = n ( n ) 2 β1l = β1r = n n r i n. (2.5)

5 : β0 R β 1 R 2.2 ỹ = β 0 + β 1 x ( ỹ i ) i = n ỹ i = (y i l i r i ) i = n n n x 2 i y i n n n n y i l i r i n n x β 0 = i y i n n y i n n ( n ) 2 n n β1 = x 2 i n n ( n ) 2. (2.6) β 0 R β 1 R 2.1 [8] β 0 = 1 0 β 1 (λ) = ỹ = β 0 + β 1 x ( ỹ i ) i = n [ n n y i (λ) n n ] y i (λ) dλ n n ( n ) 2 n n y i + (λ) β 0 β+ n 1 (λ) = n n yi (λ) β 0 y i (λ) = [y i (λ) + y+ i (λ)]/ [8] n (2.7) ỹ = β 0 + β 1 x ( ỹ i ) i = n ỹ i = (y i l i r i ) i = n n n y i n n y i 1 n 4 (l i r i ) + n n (l i r i ) β 0 = n n ) 2 β 1 = n y i β 0 n n ( n n n l i r i n n. (2.8) ỹ i = (y i µ i ) n n y i n n n y i x i y i β 0 β 0 = n n ( n ) 2 β 1 = n n n µ i n

6 630 β1. 2. β0 R β 1 R 2.2 [8] 2.2 [8] ỹ = β 0 + β 1 x ( ỹ i ) i = n n y β 0 i (λ) β n n 1 y i + (λ) β n 1 (λ) = β+ n 0 (λ) = n n 1 (n n )(yi (λ) + y+ i (λ))dλ 0 β 1 = 2 (n n ( n ) 2 ). (2.9) ỹ = β 0 + β 1 x ( ỹ i ) i = n ỹ i = (y i l i r i ) i = n ( n y i β n n n 1 l i r i ) β 0 = n n n n (n n ) y i 1 n (n n )(l i r i ) 4 β 1 = n n ) 2 (2.10) β0. ( n ỹ i = (y i µ i ) ( n y i β n n 1 µ i ) n (n n )y i β 0 = β1 = n n n n ) 2 β0. ( n (2.5) (2.6) (2.8) (2.10) ỹ = β 0 + β 1 x ỹ = β 0 + β 1 x (2.1) i ( ỹ i )

7 : 631 i ( ỹ i ). i ỹ [i] = β 0[i] + β 1[i] x β 0[i] β 1[i] R. ỹ [i] ỹ i [8] : 3.1 ỹ [i] = β 0[i] + β 1[i] x β 0[i] R β 1[i] R (x ỹ ) i = n ỹ = (y l r ) x 2 y x x y β 0[i] = (n 1) ( ) 2 x (n 1) x y x y x l x r β 1[i] = (n 1) ( ) 2 x x 2 x 2. (3.1) 3.2 ỹ [i] = β 0[i] + β 1[i] x β 0[i] R β 1[i] R (x ỹ ) i = n ỹ = (y l r ) x 2 y x x y x l x r β 0[i] = (n 1) ( ) 2 x x 2 x 2 β 1[i] = (n 1) x y x y (n 1) ( ) 2. (3.2) x 3.3 ỹ [i] = β 0[i] + β 1[i] x β 0[i] R β 1[i] R (x ỹ ) i = n ỹ = (y l r ) β 0[i] = y x x y 1 4 (l r ) + x x (l r ) (n 1) ( ) 2 x x y β 0[i] β 1[i] = x x l x r. (3.3)

8 ỹ [i] = β 0[i] + β 1[i] x β 0[i] R β 1[i] R (x ỹ ) i = n ỹ = (y µ ) x 2 y x x y β 0[i] = (n 1) ( ) 2 x x y β 0[i] x x µ x µ β 1[i] =. (3.4) 3.4 ỹ [i] = β 0[i] + β 1[i] x β 0[i] R β 1[i] R (x ỹ ) i = n ỹ = (y l r ) ( y β 1[i] x l r ) β 0[i] = n 1 n 1 n 1 ( (n 1)x ) x y 1 ( (n 1)x x )(l r ) 4 β 1[i] = (n 1) ( ) 2. (3.5) x 3.2 ỹ [i] = β 0[i] + β 1[i] x β 0[i] R β 1[i] R (x ỹ ) i = n ỹ = (y µ ) ( y β 1[i] x µ µ ) β 0[i] = n 1 n 1 β1[i] = n ( (n 1)x x )y (n 1) ( ) 2. x (3.6) ỹ [i] ỹ ( ỹ i ) ( R ỹ i R i = n) ỹ i ỹ = β 0 + β 1 x. [ 1 n s = d 2 (ỹ i n 2 ỹ 1/2 i )] (3.7) ỹ i ỹ i...

9 : n 2 β 0 β 1. i [ 1 1/2. s = d 2 (ỹ n 3 [i] ỹ [i] )] (3.8) i ỹ [i] = β 0[i] + β 1[i] x s 2 = x x y y + x x l l 2 n 3 x 2 y + x ( x y (n 1) (n 1) ( ) 2 x n 3 x x l + r 2 ) x y. (3.9) i ỹ [i] = β 0[i] + β 1[i] x s 2 = ( y β 1[i] y n ( y ( y x n 3 y β 1[i] n 1 x n 3 y β 1[i] n 1 x β 1[i] x ) 2 n 3 β 1[i] x β 1[i] x ( l )) 2 n 1 l ( r n 1 r )) 2 2. (3.10) i ỹ [i] = β 0[i] +β 1[i] x i ỹ [i] = β 0[i] + β 1[i] x. i i ; i i.

10 ỹ i.. 1 ( [8]) ỹ i = (y i l i u i ) ỹ i = (y i l i u i ) 1987 (23021) 1992 (25721) 1988 (23632) 1993 (26232) 1989 (24123) 1994 (27633) 1990 (24612) 1995 (28123) 1991 (25222) 1996 (28612) = 1986 ỹ = β 0 + β 1 x (2.6) β 0 = ( ) β1 = ỹ = ( ) x. (3.2) (3.8) i ( 2). 2 i 0 ỹ = ( ) x ỹ = ( ) x ỹ = ( ) x ỹ = ( ) x ỹ = ( ) x ỹ = ( ) x ỹ = ( ) x ỹ = ( ) x ỹ = ( ) x ỹ = ( ) x ỹ = ( ) x

11 : : 4 4. ỹ = β 0 + β 1 x (2.8) β 0 = β 1 = ( ). ỹ = ( )x. (3.4) (3.8) i ( 3). 3 i 0 ỹ = ( )x ỹ = ( )x ỹ = ( )x ỹ = ( )x ỹ = ( )x ỹ = ( )x ỹ = ( )x ỹ = ( )x ỹ = ( )x ỹ = ( )x ỹ = ( )x :

12 636 [1] Zadeh L.A. The concept of a linguistic variable and its application to approximate reasoning I II Information Sciences 8(3)(1975) (4)(1975) [2] Zadeh L.A. Fuzzy sets as a basis for a theory of possibility Fuzzy Sets and Systems 1(1)(1978) [3] Tanaa H. Uejima S. and Asai K. Linear regression analysis with fuzzy model IEEE Transactions on Systems Man and Cybernetics 12(6)(1982) [4] Diamond P. Fuzzy least squares Information Sciences 46(3)(1988) [5] Savic D.A. and Pedrycz W. Evaluation of fuzzy linear regression models Fuzzy Sets and Systems 39(1)(1991) [6] Chang Y.-H.O. and Ayyub B.M. Fuzzy regression methods a comparative assessment Fuzzy Sets and Systems 119(2)(2001) [7] : [8] (I) ( ) 42(2)(2006) [9] Diamond P. and Körner R. Extended fuzzy linear models and least squares estimates Computers & Mathematics with Applications 33(9)(1997) [10] Arabpour A.R. and Tata M. Estimating the parameters of a fuzzy linear regression model Iranian Journal of Fuzzy Systems 5(2)(2008) [11] Xu R.N. and Li C.L. Multidimensional least-squares fitting with a fuzzy model Fuzzy Sets and Systems 119(2)(2001) [12] Coppi R. D Urso P. Giordani P. and Santoro A. Least squares estimation of a linear regression model with LR fuzzy response Computational Statistics & Data Analysis 51(1)(2006) Impact Assessment for Fuzzy Linear Regression Model Based on Case Deletion Zhang Aiwu (School of Mathematical Sciences Yancheng Teachers University Yancheng ) Least squares method based on Euclidean distance and Lebesgue distance between fuzzy data is used to study parameter estimation of fuzzy linear regression model based on case deletion respectively. And the parameter estimations on two inds of distance are compared. The input of the above model is real data and output is fuzzy data. The statistical diagnosis estimation standard error of regression equations is constructed to test highly influential point or outlier in observation data. At last through identifying highly influential point or outlier in actual data it shows that the statistic constructed in this paper is effective. Keywords: Fuzzy linear regression model case deletion standard error of estimate. AMS Subject Classification: 62G68.

普通高等学校本科专业设置管理规定

普通高等学校本科专业设置管理规定普通高等学校本科专业设置申请表 ( 备案专业适用 ) 学校名称 ( 盖章 ): 学校主管部门 : 专业名称 : 浙江外国语学院浙江省教育厅金融工程专业代码 : 020302 所属学科门类及专业类 : 金融学 / 金融工程类学位授予门类 : 修业年限 :